1990 IMO Problems/Problem 4: Difference between revisions
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4. Let <math>\mathbb{Q^+}</math> be the set of positive rational numbers. Construct a function <math>f :\mathbb{Q^+}\rightarrow\mathbb{Q^+}</math> such that <math>f(xf(y)) = \frac{f(x)}{y}</math> for all <math>x, y\in{Q^+}</math>. | 4. Let <math>\mathbb{Q^+}</math> be the set of positive rational numbers. Construct a function <math>f :\mathbb{Q^+}\rightarrow\mathbb{Q^+}</math> such that <math>f(xf(y)) = \frac{f(x)}{y}</math> for all <math>x, y\in{Q^+}</math>. | ||
[[Category:Olympiad Algebra Problems]] | |||
[[Category:Functional Equation Problems]] | |||
Revision as of 07:44, 19 July 2016
4. Let 
be the set of positive rational numbers. Construct a function 
such that 
for all 
.
